Quantum Gate Noise Estimation Using Circuit Eigenvalue Sampling
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Solution Overview
Problem
Existing methods for estimating errors in quantum computers, particularly incoherent noise, are time-consuming and resource-intensive, requiring repeated sampling for each quantum gate, which ties up quantum and classical computing resources.
Innovation Solution
A method using a stochastic model to generate a linear equation for each sample run, allowing estimation of error rates with fewer samples by generating a system of equations that can be solved using linear estimation, focusing on incoherent noise through Pauli channels and eigenvalue sampling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If repeated sampling is performed for each quantum gate to estimate incoherent noise, then measurement precision is improved, but productivity deteriorates due to time-consuming and resource-intensive processes
Solution Approach 1:
The patent combines multiple individual gate measurements into a single joint measurement process. By measuring multiple gates simultaneously and using a system of linear equations to relate joint measurement outcomes to individual gate error rates, the method achieves accurate error estimation without performing separate repeated sampling for each gate, thus resolving the contradiction between measurement precision and productivity
Solution Approach 2:
The patent introduces an intermediary mathematical model (system of linear equations) that connects joint measurement outcomes to individual gate error rates. This intermediary approach allows indirect estimation of individual gate errors from collective measurements, eliminating the need for direct repeated sampling of each gate while maintaining estimation accuracy
2Reliability
If repeated sampling is performed for each quantum gate, then reliability of error estimation is improved, but loss of time increases due to resource tying
Solution Approach 1:
The patent performs preliminary setup of a mathematical model that describes the relationship between joint measurements and individual gate errors. This preliminary action enables subsequent rapid estimation of error rates without requiring time-consuming repeated sampling for each gate, thus improving reliability while reducing time loss
3Measurement precision
If comprehensive error characterization is performed for all quantum gates, then measurement precision is improved, but device complexity increases due to resource requirements
Solution Approach 1:
The patent replaces the mechanical approach of performing separate physical measurements for each gate with a computational approach using linear algebra. By substituting repeated physical sampling with mathematical computation on joint measurement data, the method achieves comprehensive error characterization while reducing the complexity of actual quantum device operations and classical post-processing
Data Source
AI summary
A method of estimating noise for individual gates of a quantum circuit uses averaged circuit eigenvalue sampling to determine an overall eigenvalue for the circuit. The circuit is sampled a sufficient number of times to fill a design matrix, wherein the design matrix allows for solving of a system of equations to determine eigenvalues for the individual gates using the averaged eigenvalue for the overall quantum circuit, the samples, and the sample results. Applying a logarithm to these relationships enables solving the system of equations using linear estimation or linear regression, in some embodiments.